PUBLICATIONS - ALEXANDRU BUIUM

Research Monographs

  • Differential Function Fields and Moduli of Algebraic Varieties, Lecture Notes in Math. 1226, Springer 1986.
  • Differential Algebraic Groups of Finite Dimension, Lecture Notes in Math. 1506, Springer 1992.
  • Differential Algebra and Diophantine Geometry, Hermann, Paris, 1994.
  • Arithmetic Differential Equations, Mathematical Surveys and Monographs 118, AMS, 2005. / Preface (pdf)

    • Published Papers

  • Espaces projectifs anisotropes et diviseurs amples, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 12, 585--586.
  • Sur les variétés dont le nombre de Picard est égal à 1, C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), no. 3, 135--137.
  • Ritt schemes and torsion theory. Pacific J. Math. 98 (1982), no. 2, 281--293.
  • Degree of the fibres of an elliptic fibration. Ann. Inst. Fourier (Grenoble) 33 (1983), no. 1, 269--276.
  • Sur le nombre de Picard des revêtements doubles des surfaces algébriques, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 8, 361--364.
  • Sur le discriminant des sections d'une variété projective singulière par des hypersurfaces de degré élevé, C. R. Acad. Sci. Paris Sér. I Math. 298 (1984), no. 4, 67--70.
  • Class groups of differential function fields. J. Algebra 89 (1984), no. 1, 56--64.
  • On surfaces of degree at most 2n+1 in P^n. Algebraic geometry (Bucharest 1982), Lecture Notes in Math., 1056, Springer, Berlin, 1984, 47-67.
  • Corps différentiels et modules des variétés algébriques, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), no. 19, 983--985.
  • Killing divisor classes by algebraisation. Ann. Inst. Fourier (Grenoble) 35 (1985), no. 2, 107--115.
  • Corps de définition des variétés algébriques et théorie de Galois pour les corps différentiels, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), no. 18, 627--629.
  • A note on the class group of surfaces in 3-space. J. Pure Appl. Algebra 37 (1985), no. 3, 229--235.
  • Movable singularities and differential Galois theory. Proceedings of the conference on algebraic geometry (Berlin, 1985), 74--80, Teubner-Texte Math., 92, Teubner, Leipzig, 1986.
  • Fields of definition of algebraic varieties in characteristic zero. Compositio Math. 61 (1987), no. 3, 339--352.
  • (with Takeuchi, M.) Rigidity of maps from Hopf algebras to group algebras. J. Algebra 118 (1988), no. 1, 14--19.
  • Birational moduli and nonabelian cohomology. Compositio Math. 68 (1988), no. 2, 175--202.
  • Birational moduli and nonabelian cohomology. II. Compositio Math. 71 (1989), no. 3, 247--263.
  • Dérivations sur les groupes algébriques, C. R. Acad. Sci. Paris Sér. I Math. 309 (1989), no. 9, 605--607.
  • Splitting differential algebraic groups. J. Algebra 130 (1990), no. 1, 97--105.
  • Intersections in jet spaces and a conjecture of S.Lang, Annals of Math. 136 (1992), 583-593.
  • Geometry of differential polynomial functions I: algebraic groups, Amer J. Math. 115, 6 (1993), 1385-1444.
  • Effective bound for the geometric Lang conjecture, Duke Math. J., 71, 2 (1993), 475-499.
  • A finiteness theorem for isogeny correspondences, in: Journes de Geometrie Algebrique d'Orsay 1992, Asterisque 218, 1993.
  • (with F.Voloch) Integral points on abelian varieties over function fields of characteristic zero, Math. Ann. 297 (1993), 303-307.
  • Geometry of differential polynomial functions II: algebraic curves, Amer J. Math. 116, 4, (1994), 785-819.
  • The abc theorem for abelian varieties, Intern. Math. Research Notices 5 (1994), 219-233.
  • On a question of B.Mazur, Duke Math. J., 75, 3, (1994), 639-644.
  • Geometry of differential polynomial functions III: moduli spaces, Amer J. Math. 117 (1995), 1-73.
  • (with F.Voloch) Reduction of the Manin map modulo p, Crelle J., 460 (1995), 117-126.
  • Differential characters of abelian varieties over p-adic fields, Invent. Math., 122, 2, (1995), 309-340.
  • Uniform bound for generic points of curves in tori, Crelle J., 469 (1995), 211-219.
  • (with F.Voloch) Mordell conjecture in characteristic p: an explicit bound, Compositio Math., 103, (1996), 1-6.
  • Geometry of p-jets, Duke Math. J., 82, 2, (1996), 349-367.
  • An approximation property for Teichmuller points, Math. Research Letters, 3 (1996), 453-457.
  • Differential characters and characteristic polynomial of Frobenius, Crelle J., 485 (1997), 209-219.
  • (with A. Pillay) A gap theorem for abelian varieties over differential fields, Math. Research Letters 4, 211-219 (1997).
  • Differential algebraic geometry and diophantine geometry: an overview, in: Symposia Math. 37, Cambridge U.P., 1997.
  • Arithmetic analogues of derivations, J. Algebra, 198, (1997), 290-299.
  • Intersection multiplicities on abelian varieties, Math. Ann. 310 (1998), 653-659.
  • Differential subgroups of simple algebraic groups over p-adic fields, Amer. J. Math. 120 (1998), 1277-1287.
  • (with P. Cassidy) Differential algebraic geometry and differential algebraic groups, in: Collected Works of Ellis Kolchin, AMS, 1999.
  • Differential Modular Forms, Crelle J., 520 (2000), 95-167.
  • Continuous p-adic functions and p-derivations, J. Number Theory, 84 (2000), 34-39.
  • Infinitesimal Mordell-Lang, J. Number Theory 90 (2001), 185-206.
  • (with M. Barcau) Siegel differential modular forms, International Math. Res. Notices, 2002, No. 28, pp.1459-1503.
  • Quotients of algebraic varieties by Zariski dense equivalence relations, in: Parshin Festschrift, Zarhin and Vostokov Eds., Contemporary Math., Vol. 300, AMS (2002), 59-97.
  • (with K. Zimmerman) Homogeneous p-differential polynomials, J. Algebra, 269 (2003), 492-507.
  • Differential modular forms on Shimura curves,I, Compositio Math. 139 (2003), 197-237.
  • Differential modular forms on Shimura curves, II: Serre operators, Compositio Math. 140 (2004), 1113-1134. .
  • Pfaffian equations satisfied by differential modular forms, Math. Res. Letters 11 (2004), 453-466.
  • Geometry of Fermat Adeles, Trans. AMS 357, 3 (2005), 901-964.
  • (with K. Zimmerman) Differential orbit spaces of discrete dynamical systems, Crelle J. 580 (2005), 201-230.
  • Complex dynamics and invariant forms mod p, International Math. Res. Notices 31 (2005), 1889-1899.
  • Finiteness results in differential algebraic geometry and diophantine geometry, chapter in: CRM Monograph Series 24, AMS, 2005.
  • A differential equation satisfied by the arithmetic Kodaira-Spencer class, J. Number Theory 119 (2006), 297-306.
  • Correspondences, Fermat quotients, and uniformization, in: Groupes de Galois arithmetiques et differentiels, Seminaires et Congres 13, Societe Mathematique de France, (2007), 70-89.
  • Differential eigenforms, J. Number Theory 128 (2008), 979-1010.
  • (with B. Poonen) Independence of points on elliptic curves arising from special points on modular and Shimura curves, I: global results, Duke Math. J., 147, 1 (2009), 181-191.
  • (with B. Poonen) Independence of points on elliptic curves arising from special points on modular and Shimura curves, II: local results, Compositio Math., 145 (2009), 566-602.
  • (with S. Simanca) Arithmetic differential equations in several variables, Annales Inst. Fourier, 59, 7 (2009), 2685-2708 (volume dedicated to B. Malgrange).
  • (with S.R. Simanca) Arithmetic Laplacians, Advances in Math. 220 (2009), 246-277.
  • (with S. R. Simanca) Arithmetic partial differential equations I, Advances in Math. 225 (2010), 689-793.
  • (with S. R. Simanca) Arithmetic partial differential equations II, Advances in Math., 225 (2010), 1308-1340.

    • Papers accepted for publication

  • Differential characters on curves, Serge Lang Memorial Volume, to appear.

    • Papers submitted for publication

  • (with C. Ralph and S.R. Simanca) Arithmetic differential operators on Z_p, submitted to J. Number Theory.
  • (with A.Saha) Hecke operators on differential modular forms mod p, submitted to J. Number Theory.
  • (with A. Saha) The ring of differential Fourier expansions, submitted to J. of Number Theory.
  • (with J. Borger) Differential forms on arithmetic jet spaces, submitted to Selecta Math.

    • Preprints

  • (with A.Saha) Differential overconvergence.

    • Other publications

  • Serge Lang's early work on Diophantine and algebraic geometry, Notices of the AMS 54, 4 (2007), 479-484.

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